Question

A boiler drum consists of a cylindrical portion 4 m long, 1.5 m in diameter, and 2.25 cm thick. It is closed by hemispherical ends. In a hydraulic test to 6 MN/m\(^2\), how many liters of additional water will be pumped in after initial filling at atmospheric pressure? The hoop strain at the junction of the cylinder and hemisphere may be assumed to be the same for both.
Consider \( E = 200 \) GN/m\(^2\); for water, \( K = 2.13 \) GN/m\(^2\) and \( 1/m = 0.3 \).

• A. 45.3
• B. 42.8
• C. 52.7
• D. 61.9

Hint:

- Consider bulk modulus for water expansion. - Use cylinder and hemisphere strain relations for accurate volume change.

Answer 1

The Correct Option is C

- Volume change formula for cylindrical and hemispherical sections: \[ \Delta V = \frac{P V}{K} + \frac{1}{E} (change \text{ in strain}) \] - Using the given values: \[ \Delta V = 52.7 \text{ liters} \]